Problem: Simplify the following expression and state the condition under which the simplification is valid: $y = \dfrac{p^2 + 4p}{p^2 - 6p - 40}$
First factor the expressions in the numerator and denominator. $ \dfrac{p^2 + 4p}{p^2 - 6p - 40} = \dfrac{(p)(p + 4)}{(p - 10)(p + 4)} $ Notice that the term $(p + 4)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(p + 4)$ gives: $y = \dfrac{p}{p - 10}$ Since we divided by $(p + 4)$, $p \neq -4$. $y = \dfrac{p}{p - 10}; \space p \neq -4$